ARLINGTON, Va. — For more than 100 years, the cremated remains of two brothers — Civil War soldiers from Indiana — sat on a funeral home shelf, unclaimed and largely forgotten.

On Thursday, their remains were given a final resting place at Arlington National Cemetery, which dedicated a new columbarium court designed to hold the cremated remains of more than 20,000 eligible service members and family.

It is the ninth columbarium court at Arlington, where roughly 400,000 are interred.

The first six remains to be interred at the court were recovered by the Missing In America Project, an organization based in Grants Pass, Ore., that scours funeral homes across the country to recover remains of veterans that have gone unclaimed....